Introduction

Chemical kinetics is the discipline concerning the time rate of change of the concentration of chemical species through the course of a chemical reaction. The typical approach to chemical kinetics problems is first to note the elementary steps and then to express the time rate of change of the concentration of each chemical species as a sum of its sources and sinks. The result is a system of coupled, often nonlinear, differential equations. This set of equations is subsequently simplified by appropriate approximations, and the reduced set of equations is solved analytically or numerically, as appropriate. For example, for the reaction , we can write where k is the rate constant. The solution for A[t] readily follows as where is the initial concentration of A.

The chemical kinetics of the reaction are thus readily understood, and an analytical solution is easily obtained. Many chemical reactions are much more complex, and an understanding of the coupled differential equations is more difficult. A fascinating chemical reaction is the Belousov-Zhabotinskii reaction, discovered first in 1958 and again in 1964. Prior to its discovery, esteemed chemists argued that oscillating chemical reactions could not occur. In the Belousov-Zhabotinskii reaction, when the proper concentrations of bromate, malonic acid, sulfuric acid, and cerium ions are mixed together, the color of the solution oscillates from yellow to clear with a period of about two minutes for several hours. How can this reaction be understood? Many fundamental chemical measurements have been made over the last three decades to obtain the rate constants of the elementary steps, and twenty-one important steps have been identified. In addition, the resulting system of coupled differential equations has been numerically integrated to reproduce the observed oscillations. However, obtaining an intuitive understanding of this complex system is difficult for the novitiate. One successful approach in the past has been through chaos theory, invoking an oregonator model. In this paper, a general chemical kinetics solver for Mathematica is introduced. Then, the powerful numerical engine and graphic capabilities of Mathematica are employed to understand the Belousov-Zhabotinskii reaction.